Learning pure quantum states (almost) without regret
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915325795106816 |
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| author | Lumbreras, Josep Terekhov, Mikhail Tomamichel, Marco |
| author_facet | Lumbreras, Josep Terekhov, Mikhail Tomamichel, Marco |
| contents | We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time making sure that the post-measurement state of the samples is only minimally perturbed? Defining regret as the cumulative disturbance of all samples, the challenge is to find a balance between the most informative sequence of measurements on the one hand and measurements incurring minimal regret on the other. Here we answer this question for qubit states by exhibiting a protocol that for pure states achieves maximal precision while incurring a regret that grows only polylogarithmically with the number of samples, a scaling that we show to be optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning pure quantum states (almost) without regret Lumbreras, Josep Terekhov, Mikhail Tomamichel, Marco Quantum Physics Artificial Intelligence Machine Learning We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time making sure that the post-measurement state of the samples is only minimally perturbed? Defining regret as the cumulative disturbance of all samples, the challenge is to find a balance between the most informative sequence of measurements on the one hand and measurements incurring minimal regret on the other. Here we answer this question for qubit states by exhibiting a protocol that for pure states achieves maximal precision while incurring a regret that grows only polylogarithmically with the number of samples, a scaling that we show to be optimal. |
| title | Learning pure quantum states (almost) without regret |
| topic | Quantum Physics Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2406.18370 |